A065206 Numbers which need one 'Reverse and Add' step to reach a palindrome.

10, 12, 13, 14, 15, 16, 17, 18, 20, 21, 23, 24, 25, 26, 27, 29, 30, 31, 32, 34, 35, 36, 38, 40, 41, 42, 43, 45, 47, 50, 51, 52, 53, 54, 56, 60, 61, 62, 63, 65, 70, 71, 72, 74, 80, 81, 83, 90, 92, 100, 102, 103, 104, 105, 106, 107, 108, 110, 112, 113, 114, 115, 116, 117

Offset

1,1

Comments

The number of steps starts at 0, so palindromes (A002113) are excluded.

Numbers k such that A033665(k) = 1. - Andrew Howroyd, Dec 05 2024

Links

Harry J. Smith, Table of n, a(n) for n = 1..1000

Index entries for sequences related to Reverse and Add!

Mathematica

Select[Range[10, 120], !PalindromeQ[#]&&PalindromeQ[#+IntegerReverse[#]]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jun 14 2017 *)

Prog

(ARIBAS): function revadd_steps(k, stop: integer); var c, n, m, steps, rev: integer; begin n := 0; c := 0; while c < stop do m := n; rev := int_reverse(m); steps := 0; while steps < k and m <> rev do m := m + rev; rev := int_reverse(m); inc(steps); end; if steps = k and m = rev then write(n, " "); inc(c); end; inc(n); end; end; revadd_steps(1, 66).
(Haskell)
a065206 n = a065206_list !! (n-1)
a065206_list = filter ((== 1) . a136522 . a056964) a029742_list
-- Reinhard Zumkeller, Oct 14 2011
(PARI) isok(n, s=1)={for(k=0, s, my(r=fromdigits(Vecrev(digits(n)))); if(r==n, return(k==s)); n += r); 0} \\ Andrew Howroyd, Dec 05 2024

Crossrefs

Cf. A002113, A015976, A033665, A136522, A056964, A029742.

Sequences for 2..12 steps needed are: A065207, A065208, A065209, A065210, A065211, A065212, A065213, A065214, A065215, A065216, A065217.

Sequence in context: A059504 A083310 A367797 * A261925 A083476 A124404

Adjacent sequences: A065203 A065204 A065205 * A065207 A065208 A065209

Keyword

nonn,base

Author

Klaus Brockhaus, Oct 21 2001

Extensions

Offset corrected by Harry J. Smith, Oct 13 2009

Status

approved